A different and less beautiful solution to the Entscheidungsproblem, with the clunkier name “untyped lambda calculus,” had been published earlier that year by Alonzo Church, a mathematician at Princeton. Turing’s professor Max Newman decided that it would be useful for Turing to go there to study under Church. In his letter of recommendation, Newman described Turing’s enormous potential. He also added a more personal appeal based on Turing’s personality. “He has been working without any supervision or criticism from anyone,” Newman wrote. “This makes it all the more important that he should come into contact as soon as possible with the leading workers on this line, so that he should not develop into a confirmed solitary.”¹¹

Turing did have a tendency toward being a loner. His homosexuality made him feel like an outsider at times; he lived alone and avoided deep personal commitments. At one point he proposed marriage to a female colleague, but then felt compelled to tell her that he was gay; she was unfazed and still willing to get married, but he believed it would be a sham and decided not to proceed. Yet he did not become “a confirmed solitary.” He learned to work as part of a team, with collaborators, which was key to allowing his abstract theories to be reflected in real and tangible inventions.

In September 1936, while waiting for his paper to be published, the twenty-four-year-old doctoral candidate sailed to America in steerage class aboard the aging ocean liner RMS Berengaria, lugging with him a prized brass sextant. His office at Princeton was in the Mathematics Department building, which also then housed the Institute for Advanced Study, where Einstein, Gödel, and von Neumann held court. The cultivated and highly sociable von Neumann became particularly interested in Turing’s work, despite their very different personalities.

The seismic shifts and simultaneous advances of 1937 were not directly caused by the publication of Turing’s paper. In fact, it got little notice at first. Turing asked his mother to send out reprints of it to the mathematical philosopher Bertrand Russell and a half dozen other famous scholars, but the only major review was by Alonzo Church, who could afford to be flattering because he had been ahead of Turing in solving Hilbert’s decision problem. Church was not only generous; he introduced the term Turing machine for what Turing had called a Logical Computing Machine. Thus at twenty-four, Turing’s name became indelibly stamped on one of the most important concepts of the digital age.¹²

CLAUDE SHANNON AND GEORGE STIBITZ AT BELL LABS

There was another seminal theoretical breakthrough in 1937, similar to Turing’s in that it was purely a thought experiment. This one was the work of an MIT graduate student named Claude Shannon, who that year turned in the most influential master’s thesis of all time, a paper that Scientific American later dubbed “the Magna Carta of the Information Age.”¹³

Shannon grew up in a small Michigan town where he built model planes and amateur radios, then went on to major in electrical engineering and math at the University of Michigan. In his senior year he answered a help-wanted listing tacked to a bulletin board, which offered a job at MIT working under Vannevar Bush helping to run the Differential Analyzer. Shannon got the job and was mesmerized by the machine—not so much the rods and pulleys and wheels that formed the analog components as the electromagnetic relay switches that were part of its control circuit. As electrical signals caused them to click open and clack closed, the switches created different circuit patterns.

During the summer of 1937, Shannon took a break from MIT and went to work at Bell Labs, a research facility run by AT&T. Located then in Manhattan on the Hudson River edge of Greenwich Village, it was a haven for turning ideas into inventions. Abstract theories intersected with practical problems there, and in the corridors and cafeterias eccentric theorists mingled with hands-on engineers, gnarly mechanics, and businesslike problem-solvers, encouraging the cross-fertilization of theory with engineering. This made Bell Labs an archetype of one of the most important underpinnings of digital-age innovation, what the Harvard science historian Peter Galison has called a “trading zone.” When these disparate practitioners and theoreticians came together, they learned how to find a common parlance to trade ideas and exchange information.¹⁴

At Bell Labs, Shannon saw up close the wonderful power of the phone system’s circuits, which used electrical switches to route calls and balance loads. In his mind, he began connecting the workings of these circuits to another subject he found fascinating, the system of logic formulated ninety years earlier by the British mathematician George Boole. Boole revolutionized logic by finding ways to express logical statements using symbols and equations. He gave true propositions the value 1 and false propositions a 0. A set of basic logical operations—such as and, or, not, either/or, and if/then—could then be performed using these propositions, just as if they were math equations.

Shannon figured out that electrical circuits could execute these logical operations using an arrangement of on-off switches. To perform an and function, for example, two switches could be put in sequence, so that both had to be on for electricity to flow. To perform an or function, the switches could be in parallel so that electricity would flow if either of them was on. Slightly more versatile switches called logic gates could streamline the process. In other words, you could design a circuit containing a lot of relays and logic gates that could perform, step by step, a sequence of logical tasks.

(A “relay” is simply a switch that can be opened and shut electrically, such as by using an electromagnet. The ones that clack open and closed are sometimes called electromechanical because they have moving parts. Vacuum tubes and transistors can also be used as switches in an electrical circuit; they are called electronic because they manipulate the flow of electrons but do not require the movement of any physical parts. A “logic gate” is a switch that can handle one or more inputs. For example, in the case of two inputs, an and logic gate switches on if both of the inputs are on, and an or logic gate switches on if either of the inputs is on. Shannon’s insight was that these could be wired together in circuits that could execute the tasks of Boole’s logical algebra.)

When Shannon returned to MIT in the fall, Bush was fascinated by his ideas and urged him to include them in his master’s thesis. Entitled “A Symbolic Analysis of Relay and Switching Circuits,” it showed how each of the many functions of Boolean algebra could be executed. “It is possible to perform complex mathematical operations by means of relay circuits,” he summed up at the end.¹⁵ This became the basic concept underlying all digital computers.

Shannon’s ideas intrigued Turing because they neatly related to his own just-published concept of a universal machine that could use simple instructions, expressed in binary coding, to tackle problems not only of math but of logic. Also, since logic was related to the way human minds reason, a machine that performed logical tasks could, in theory, mimic the way humans think.

Working at Bell Labs at the same time was a mathematician named George Stibitz, whose job was to figure out ways to handle the increasingly complicated calculations needed by the telephone engineers. The only tools he had were mechanical desktop adding machines, so he set out to invent something better based on Shannon’s insight that electronic circuits could perform mathematical and logical tasks. Late one evening in November, he went to the stockroom and took home some old electromagnetic relays and bulbs. At his kitchen table, he put the parts together with a tobacco tin and a few switches to form a simple logical circuit that could add binary numbers. A lit bulb represented a 1, and an unlit bulb represented a 0. His wife dubbed it the “K-Model,” after the kitchen table. He took it into the office the next day and tried to convince his colleagues that, with enough relays, he could make a calculating machine.